The Spaniard, 29, has fallen after losing to world number one Novak Djokovic in the French Open quarter-finals last week.
It is Nadal's lowest ranking since he was 11th as a teenager in April 2005.
Swiss Stan Wawrinka, who beat Djokovic to the Roland Garros men's singles title on Sunday, climbs to fourth.
Despite his defeat, 28-year-old Djokovic stays ahead of Switzerland's Roger Federer and Britain's Andy Murray, who was beaten by the Serb in the last four.
Serena Williams, who claimed her 20th Grand Slam singles' title, increased her margin at the top of the women's rankings.
The 33-year-old American's nearest rival is Czech Petra Kvitova, who has risen from fourth.
Russian Maria Sharapova, 28, drops two places to fourth following her fourth-round loss to eventual finalist Lucie Safarova, 28, with the Czech player moving to a career-best seventh.